That's a very narrow description of a DAW. OP was specifically talking about the piano roll - a feature that obviously differs from traditional notation but is still very much related since both aim to achieve the same goal.
A DAW surely isn't limited to sample-based arrangements. In that light your description of a DAW isn't wrong, but very much unrelated to the point OP was trying to make.
A DAW surely isn't limited to sample-based arrangements. In that light your description of a DAW isn't wrong, but very much unrelated to the point OP was trying to make.